# LogNormal Distribution

## Log-normal

The log-normal distribution has the probability density function (PDF):

$f(x\mid \mu ,\sigma ^{2}) = \frac 1 {x\sigma\sqrt{2\pi}}\ \exp\left(-\frac{\left(\ln x-\mu\right)^2}{2\sigma^2}\right) \,,\quad x>0 \,,$

where $$\mu\in\mathbb{R}$$ and $$\sigma > 0$$ are the parameters associated with the Normal distribution. The mean of the PDF is $$\exp(\mu+\frac{\sigma^2}{2})$$.

## Usage

e["Distribution"][*index*]["Type"] = "Univariate/LogNormal"

## Distribution Configuration

These are settings required by this distribution.

Mu
Sigma

## Configuration

These are settings required by this module.

Name
• Usage: e[“Name”] = string

• Description: Defines the name of the distribution.

Random Seed
• Usage: e[“Random Seed”] = unsigned integer

• Description: Defines the random seed of the distribution.

Range
• Usage: e[“Range”] = gsl_rng

• Description: Stores the current state of the distribution in hexadecimal notation.

## Default Configuration

These following configuration will be assigned by default. Any settings defined by the user will override the given settings specified in these defaults.

{
"Name": "",
"Random Seed": 0,
"Range": ""
}